Problem: Rewrite as a simplified fraction. ${2.\overline{53} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 253.5353...\\ 1x &= 2.5353...\end{align*}}$ Subtracting the two equations, we have: ${99x = 251}$ ${x = \dfrac{251}{99}} \text{or} {2 \dfrac{53}{99}}$